Have you been changing the water frequently, as in daily? Roots need to breath just like animals do, and if you let the water go stagnant they won't be able to pull any oxygen from it and the roots will essentially drown.

Generally, as soon as you see it starting to root, take it out and put it in some soil. Even if you keep changing the water out to get more roots, they're going to be taproots, not feeder roots, and won't help the plant in any way when you do transfer it out. Better to transplant early while its still growing roots so that it can establish itself and grow healthy roots the way nature intended.

Oh ok. Thanks so much! So even though they have been brown a few days now, will they still grow in soil? Or should i just throw them out and try a new batch in soil this time? Also, how long will it take thyme to root in soil?

Replace the water with properly aerated water (which basically just means turn the tap on full blast so it has lots of bubbles in it), see if it perks up and starts growing more new white roots. If it does, go ahead and stick the cutting in soil, its ready to go.